Question

Construct a combined histogram and frequency polygon for the following frequency distribution:

Class-intervals	20-30	30-40	40-50	50-60	60-70
Frequency	8	12	15	10	3

Answer 1

Steps to construct a combined histogram and frequency polygon is as follows:

• Draw two mutually perpendicular axes, the X-axis and Y-axis, intersecting at the origin O.
• Mark the class intervals (10-20, 20-30, ... 70-80) along the X-axis taking a suitable scale.
• Mark the corresponding frequencies (0, 2, 4, ... 16) along the Y-axis taking a suitable scale.
• Construct contiguous rectangles with bases as class intervals and heights proportional to their frequencies.
• Locate and mark the midpoints of the top horizontal sides of each rectangle drawn in the previous step  [Identifying points (25, 8), (35, 12), (45, 15), (55, 10), and (65, 3)]
• Take an imagined class interval 10-20 preceding the first class and mark its midpoint at frequency 0.
• Take an imagined class interval 70-80 succeeding the last class and mark its midpoint at frequency 0.
• Join all these consecutive midpoints, including the anchor points, using straight line segments.